Urban retail dynamics: insights from percolation theory and spatial interaction modelling

The study of the properties and structure of a city’s road network has for many years been the focus of much work, as has the mathematical modelling of the location of its retail activity and of the emergence of clustering in retail centres. Despite these two phenomena strongly depending on one another and their fundamental importance in understanding cities, little work has been done in order to compare their evolution and their local and global properties. The contribution of this paper aims to highlight the strong relationship that retail dynamics have with the hierarchical structure of the underlying road network. We achieve this by comparing the results of the entropy maximising retail model with a percolation analysis of the road network in the city of London. We interpret the great agreement in the hierarchical spatial organisation outlined by these two approaches as new evidence of the interdependence of these two crucial dimensions of a city’s life.

[1]  D. Huff.  A Programmed Solution for Approximating an Optimum Retail Location , 1966 .

[2]  Alan Wilson,et al.  A statistical theory of spatial distribution models , 1967 .

[3]  B. Berry,et al.  Central places in Southern Germany , 1967 .

[4]  Alan Wilson,et al.  Entropy in urban and regional modelling , 1972, Handbook on Entropy, Complexity and Spatial Dynamics.

[5]  H. Stanley,et al.  Site-Bond Correlated-Percolation Problem: A Statistical Mechanical Model of Polymer Gelation , 1979 .

[6]  D. McFadden.  Econometric Models for Probabilistic Choice Among Products , 1980 .

[7]  Alan Wilson,et al.  The Corner-Shop to Supermarket Transition in Retailing: The Beginnings of Empirical Evidence , 1983 .

[8]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[9]  Stephen Brown.  A Perceptual Approach to Retail Agglomeration , 1987 .

[10]  J. Luck,et al.  The electrical conductivity of binary disordered systems, percolation clusters, fractals and related models , 1990 .

[11]  Christensen,et al.  Self-organized critical forest-fire model: Mean-field theory and simulation results in 1 to 6 dimenisons. , 1993, Physical review letters.

[12]  H. Stanley,et al.  Predicting oil recovery using percolation , 1999 .

[13]  A. Rivlin,et al.  Economic Choices , 2001 .

[14]  M. Newman,et al.  Percolation and epidemics in a two-dimensional small world. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  H. Larralde,et al.  Aggregation of retail stores , 2005 .

[16]  Vito Latora,et al.  The network analysis of urban streets: A dual approach , 2006 .

[17]  Pablo Jensen.  Network-based predictions of retail store commercial categories and optimal locations. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  V. Latora,et al.  Structural properties of planar graphs of urban street patterns. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Alan Wilson,et al.  Boltzmann, Lotka and Volterra and spatial structural evolution: an integrated methodology for some dynamical systems , 2008, Journal of The Royal Society Interface.

[20]  Alessandro Flammini,et al.  Modeling urban street patterns. , 2007, Physical review letters.

[21]  Beom Jun Kim,et al.  Scaling laws between population and facility densities , 2009, Proceedings of the National Academy of Sciences.

[22]  V. Latora,et al.  Street Centrality and Densities of Retail and Services in Bologna, Italy , 2009 .

[23]  Marc Barthelemy,et al.  Spatial Networks , 2010, Encyclopedia of Social Network Analysis and Mining.

[24]  Alan Wilson,et al.  A Framework for Exploring Urban Retail Discontinuities. 探索城市零售业不连续性的框架 , 2011 .

[25]  Alan Wilson,et al.  Phase transitions and path dependence in urban evolution , 2011, J. Geogr. Syst..

[26]  Mariano Sigman,et al.  A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks , 2011, Proceedings of the National Academy of Sciences.

[27]  Mariano Sigman,et al.  Collective behavior in the spatial spreading of obesity , 2012, Scientific Reports.

[28]  V. Latora,et al.  Street Centrality and the Location of Economic Activities in Barcelona , 2012 .

[29]  Marc Barthelemy,et al.  Emergence of hierarchy in cost-driven growth of spatial networks , 2013, Proceedings of the National Academy of Sciences.

[30]  M. Barthelemy,et al.  A typology of street patterns , 2014, Journal of The Royal Society Interface.

[31]  Yunpeng Wang,et al.  Percolation transition in dynamical traffic network with evolving critical bottlenecks , 2014, Proceedings of the National Academy of Sciences.

[32]  Michael Batty,et al.  Multifractal to monofractal evolution of the London street network. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  M. Batty,et al.  Cities and regions in Britain through hierarchical percolation , 2015, Royal Society Open Science.

[34]  A. Wilson.  in the Theory of Trip Distribution, Mode Split and Route Split , 2016 .

[35]  V. Latora,et al.  Spatio-Temporal Analysis of Micro Economic Activities in Rome Reveals Patterns of Mixed-Use Urban Evolution , 2016, PloS one.

[36]  H. Kral.  Boltzmann , 2020, Catalysis from A to Z.